Torsional and Aileron Flutter

Abstract

The aim of this paper is to find an approximate solution of the influence of various elements on the critical frequency in a binary system of torsional and aileron vibration. Assuming the system as a nonconservative one and taking into account the results obtained by von Karman and Biot, the influence of the kind of material and shape and airfoil thickness on the torsional frequency is considered. I t is to be noted that damping is not taken into account. The idea of wing torsional is introduced, being inversely proportional to the angle of twist at the end of the wing. The problem of influence of the kind of material, aspect ratio and span, taper and airfoil thickness on the torsional frequency is solved in a first approximation from the point of view of proportion. Finally, the influence of various materials of and aileron is taken into consideration. An at tempt is made to solve this problem by the aid of the partial differential equation based on Newton's Law. The equation is applied to an oscillating rod and permits the first natural frequency of the oscillating rod to be found. Using the Membrane Analogy, the differential equation is applied to a tubular member. The results are checked by the aid of Rayleigh's Method. The following conclusions are drawn: (a) With regard to the influence of the kind of material on the binary system of torsional and aileron vibration, the decisive factor is the ratio of modulus of rigidity to the specific weight. High values of this ratio are obtained for steel and magnesium alloys; wood has the lowest ratio. (b) The influence of span and airfoil thickness are significant and the influence of taper is less important. (c) When a tubular member consists of various materials, a decisive factor is also the ratio of the modulus of rigidity to the specific weight. The following combinations might be advantageous: aluminum alloy or magnesium alloy and steel aileron, spruce-plywood and metal aileron. (d) Three different methods lead to the same result—that, from a system of torsional oscillation standpoint, the decisive factor is the ratio of the modulus of rigidity to the specific weight. The methods include the computations based on the magnitude of the torsional frequency given by von Karman and Biot, the differential equation based on Newton's Law, and Rayleigh's Method. (e) The results obtained cannot be applied directly to practice because of the fact that damping, an important factor from flutter point of view, was not taken into account. la maia